I have a bunch of IID samples from a random variable with unknown mean and unknown variance. I now need to know the variance of the average of these samples.
I found some references. In decreasing order of helpfulness: 1, 2, 3. These give a formula for the variance in terms of the variance of the original distribution. What I haven't been able to find is a direct solution for the case of the original distribution having unknown variance. This similar question may be of use, but I am unsure how to apply it.
My first thought is to try to use the sample variance as an estimate for the population variance. My question is, is that the right way to do it? Is so, how do I correct for any differences? If not, what is the right way?